**ERIC Number:**EJ748991

**Record Type:**Journal

**Publication Date:**2006-Jun

**Pages:**15

**Abstractor:**Author

**ISBN:**N/A

**ISSN:**ISSN-0033-3123

Some Results on Mean Square Error for Factor Score Prediction

Krijnen, Wim P.

Psychometrika, v71 n2 p395-409 Jun 2006

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix gamma[subscript rho] = theta[superscript 1/2] lambda[subscript rho] 'psi[subscript rho] [superscript -1] lambda[subscript rho] theta[superscript 1/2]. This matrix increases with the number of observable variables rho. A necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of gamma rho or, equivalently, divergence of signal-to-noise (Schneeweiss & Mathes, 1995). The same condition is necessary and sufficient for convergence to zero of the positive definite MSE differences of factor predictors, convergence to zero of the distance between factor predictors, and convergence to the unit value of the relative efficiencies of predictors. Various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors.

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A